Introduction:
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Many challenging problems in the theory of nonlinear lattices and periodic partial differential equations arise from the modeling of nonlinear media with microstructure, such as photonic or phononic crystals, granular media and composite materials. Among many fundamental problems, this minisymposium will address the existence and qualitative properties of periodic or localized waves (solitary waves and breathers) in these systems. Topics will include dynamical stability, wave scattering by defects, trapping of propagating waves, and nontrivial modes of propagation such as direction-reversing waves.
The important questions to be discussed are on how wave propagation can be influenced by the microstructure and can be potentially controlled. The minisymposium will emphasize a variety of analytical approaches, such as modulation equations, homogenization, reduced-order models, variational methods, and the rigorous derivation of lattice differential equations from periodic PDE.
In the context of granular media, we will address new types of analytical difficulties linked with nonsmooth contact interactions and purely nonlinear energy propagation in the absence of phonon modes. Computational approaches and experimental results will be also presented. |
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